On differentiability of the Parisi formula
Dmitry Panchenko
TL;DR
This paper provides a simplified proof of the differentiability of the Parisi formula for the SK model's free energy and demonstrates its application in showing non self-averaging of the overlap.
Contribution
It offers a more straightforward proof of the Parisi formula's differentiability and applies this to analyze overlap behavior outside the replica symmetric region.
Findings
Simplified proof of Parisi formula differentiability
Application to non self-averaging of the overlap
Insights into replica symmetry breaking
Abstract
It was proved by Michel Talagrand in [10] that the Parisi formula for the free energy in the Sherrington-Kirkpatrick model is differentiable with respect to inverse temperature parameter. We present a simpler proof of this result by using approximate solutions in the Parisi formula and give one example of application of the differentiability to prove non self-averaging of the overlap outside of the replica symmetric region.
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Taxonomy
TopicsTheoretical and Computational Physics · Advanced Thermodynamics and Statistical Mechanics · Stochastic processes and statistical mechanics